Solution

Ratio of Rajiv, Sanju and Tanu investment with respect to the time =(z-400) x4+(100-50) % of (z-400) x8 : (z-1000)x4+(100+30)% of (z-1000)x8 : (z+200)x4+(z+200-y)x8    Eq.(i) The profit share of Sanju will be 50% more than the profit share of Rajiv. profit share of Sanju = (100+50) % of profit share of Rajiv the profit share of Sanju = 150% of the profit share of Rajiv profit share of Sanju = 1.5 x (profit share of Rajiv) the profit share of Sanju: profit share of Rajiv = 1.5/1 = 15/10 = 3:2    Eq.(ii) At the end of one year, the profit share of Sanju and Tanu will be the same. profit share of Sanju: profit share of Tanu ⇒ 3:3    Eq.(iii) From Eq.(ii) and Eq.(iii), the profit share of Rajiv: profit share of Sanju: profit share of Tanu ⇒ 2:3:3    Eq.(iv) From Eq.(i) and Eq.(iv). [(z-400)x4+(100-50)% of (z-400)x8]/[(z-1000)x4+(100+30)% of (z-1000)x8] = 2/3 [(z-400)x4+50% of (z-400)x8]/[(z-1000)x4+130% of (z-1000)x8] = 2/3 [(z-400) x4+0.5(z-400) x8]/[(z-1000)x4+1.3(z-1000)x8] = ⅔ So,  z = 4000 Put the value of ‘z’ in Eq.(i) The ratio of Rajiv, Sanju, and Tanu investment with respect to the time ⇒ (4000-400) x4+(100-50) % of (4000-400) x8: (4000-1000)x4+(100+30)% of (4000-1000)x8 : (4000+200)x4+(4000+200-y)x8 ⇒ 3600x4+50% of 3600x8: 3000x4+130% of (3000) x8: (4200) x4+(4200-y) x8 ⇒ 3600+50% of 3600x2: 3000+130% of (3000) x2: (4200) +(4200-y) x2 ⇒ 3600+1800x2: 3000+3900x2: (4200) +(4200-y) x2 ⇒ 3600+3600: 3000+7800: (4200) +(8400-2y) ⇒ 7200: 10800: (12600-2y) …. Eq.(v) From Eq.(iii) and Eq.(v). 10800 / (12600-2y) = 3/3 10800 = (12600-2y) 10800 = (12600-2y) 2y = 12600-10800 = 1800 y = 9 00 a) 5y = (z+800) 5x900 = (4000+800) 4500 = 4800 The above equation is not satisfied. So, this is not the correct answer. b) (z+200)/7 = y (4000+200)/7 = 900 4200/7 = 600 600 = 900 The above equation is satisfied. So, this is not the correct answer. c) 6y = (z+200) 6x900 = (4000+200) 5400 = 4200 The above equation is not satisfied. So this is not the correct answer. d) (z+400)/6 = 1.5y (4000+400)/6 = 1.5x900 (4000+400)/6 = 900 4400 = 8100 The above equation is not satisfied. So, this is not the correct answer.